Problem: Simplify the following expression: $ a = \dfrac{4}{7} + \dfrac{5t + 2}{-9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9}{-9}$ $ \dfrac{4}{7} \times \dfrac{-9}{-9} = \dfrac{-36}{-63} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{5t + 2}{-9} \times \dfrac{7}{7} = \dfrac{35t + 14}{-63} $ Therefore $ a = \dfrac{-36}{-63} + \dfrac{35t + 14}{-63} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-36 + 35t + 14}{-63} $ $a = \dfrac{35t - 22}{-63}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-35t + 22}{63}$